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Do you have specific place you need to go? Without the reflexive, it may only makes sense with a particular destination, like “Tengo que ir al médico mañana,” or rather more rarely perhaps if you’re making a progressive tense, like “Tengo que ir cantando toda la noche,” as might be the case if you were in a tuna.

Otherwise, a reflexive “Tengo que irme” makes more sense, if what you mean is that you have to leave somewhere.

I guess there’s also “Tengo que mear”, but that’s a difference sense of “having to go”. And you probably don’t want to make that one reflexive. :)